CMM-2003 – Computer Methods in Mechanics June 3-6, 2003, Gliwice, Poland Discrete element model of sand mould manufacture for Lost Foam Casting process Jerzy Rojek Institute of FundamentalTechnological Research Swietokrzyska 21, 00-049 Warsaw, Poland e-mail: jrojek@ippt.gov.pl Carlos Agelet de Saracibar and Francisco Zarate International Center for Numerical Methods in Engineering, CIMNE J. Girona 1-3, 08034 Barcelona, Spain e-mail: zarate@ cimne.upc.es; agelet@ cimne.upc.es Abstract Discrete element model of mould manufacture for the lost foam casting process is presented. The main phenomena modelled are filling of a mould with sand and sand compaction by vibration. Sand is modeled as collection of spherical (in 3D) or cylindrical (in 2D) particles. Numerical simulation predicts defects of the mould due to insufficient sand compaction around the pattern, as well as possible distortion of the pattern during mould filling and compaction. Numerical results are compared with experimental data. Keywords: lost foam casting, mould manufacture, discrete element method, granular flow, sand compaction 1. Introduction Lost foam casting (LFC) is a type of metal casting process that uses a sand mould with a polystyrene foam pattern remaining in the mould during metal pouring. The foam pattern is replaced by molten metal, producing the casting. The production of moulds for LFC process involves three steps. It is started with the placement of the pattern in the moulding box. Next, the pattern is covered with dry and unbonded sand. Then the compaction of the sand is achieved by a vibration process. Once the compaction is complete, the mould is ready to be poured. Vibratory compaction is one of the most important phases of the LFC process and it may be critical to obtain a good quality cast product. Vibration should ensure uniform and proper compaction, by filling all the cavities with the sand and packing sand to maximum density around the pattern. There is no simple relationship between sand parameters and vibration process parameters, therefore the compaction process is often designed in a purely empirical trial and error manner. Other defects occurring in the LFC process are the shape defects due to deformation of pattern under sand pressure during filling and the vibration process. This phenomenon has also been studied in our numerical model. 2. Main assumptions The objective of the computational model developed is to provide a more rational way to design the filling and compaction process. The main physical phenomenon considered is the flow of granular material (sand) around a rigid or deformable obstacle (moulding box, pattern) under gravity or vibration. Numerical models of sand compaction adopted in the present study are based on the discrete element method (DEM) which is widely recognized as a suitable tool to model granular materials [1], [2]. Within the DEM, it is assumed that the casting sand in the LFC process can be represented as a collection of rigid particles (spheres or balls in 3D and discs in 2D) interacting among themselves in the normal and tangential directions, due to friction. To allow us to predict the cellular foam pattern deformation during mould filling and compaction the Discrete Element Method is combined with the Finite Element Method. A general model consists of discrete elements representing sand and finite elements discretising a deformable pattern. 3. Discrete Element Method formulation The DEM scheme using spherical rigid elements has been introduced by Cundall [1, 3]. Our study is based on our own implementation of the DEM in the finite element explicit dynamic code Simpact [4]. The translational and rotational motion of rigid spherical or cylindrical particles is described by means of Newton-Euler equations of rigid body dynamics. Equations of motion are integrated in time using the central difference scheme. Explicit integration in time yields high computational efficiency. Its known disadvantage is the conditional numerical stability imposing the limitation on the time step. Normal and tangential contact forces between particles are obtained using a simple constitutive model formulated for the contact between two rigid spheres. The normal contact force is decomposed to the elastic and damping parts. The elastic part is proportional to the penetration of the two particles. The contact damping force is assumed to be of viscous type proportional to the normal relative velocity of the centres of the two particles in contact. Contact damping dissipates kinetic energy of contacting particles. The tangential contact force is brought about by friction opposing the relative motion at the contact point. Friction is modelled using regularized Coulomb law. The sliding friction cannot provide any resistance to the movement of the sphere (cylinder) rolling on a rough surface if there is no relative tangential velocity at the contact point. The rolling resistance can be simulated numerically by assuming some eccentricity of the normal reaction and applying the resisting moment proportional to this eccentricity.